For a more modern approach (that's one of those rare cases where things have gotten more powerful while getting simpler over the years): https://www.youtube.com/c/TenMinutePhysics/videos (by basically the inventor of PBD, which he barely even mentions/brags about).
I've been experimenting with webgl ragdoll physics based loosely on Takahiro Harada's GPU Gems article, but I'm nowhere near the "puppetmaster" stage yet ;)
Position based dynamics :) With normal `next_pos = current_pos + velocity * dt` schemes you can get instabilities and it can be non obvious how to implement certain physics phenomena. With PBD you basically define a 'constraint' that particles have to satisfy (e.g. rigid lengths become a 'distances between points must be X') and then you solve for a valid configuration in between renders (basically with gradients descent, though you solve for roots so it becomes newtons method).
For a more lay explanation you solve constraints directly by moving elements around and using the difference between their current position and previous position as their velocity. If you've some experience of numerical integration it's quite similar to verlet integration. This approach is good because it lets you have constraints with infinite stiffness without the simulation exploding.
The original papers consider points (like a mass-spring system) but it's also been extended to rigidbodies.
I'm new to physics engines—I just started figuring out how to upgrade my simple grid cellular automata engine to a 2D engine for my toy sim tool (https://github.com/breck7/simoji) —and have been surprised by existing implementations, because it just seems not how the universe actually computes. I had not seen PBD before and it seems to be a closer model.
